- : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] double(0) -> 0 [2] double(s(x)) -> s(s(double(x))) [3] +(x,0) -> x [4] +(x,s(y)) -> s(+(x,y)) [5] +(s(x),y) -> s(+(x,y)) [6] double(x) -> +(x,x) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> --> --> --> } APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { double(0) >= 0 ; double(s(x)) >= s(s(double(x))) ; double(x) >= +(x,x) ; +(s(x),y) >= s(+(x,y)) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; Marked_double(s(x)) >= Marked_double(x) ; } + Disjunctions:{ { Marked_double(s(x)) > Marked_double(x) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: double(0) >= 0 constraint: double(s(x)) >= s(s(double(x))) constraint: double(x) >= +(x,x) constraint: +(s(x),y) >= s(+(x,y)) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: Marked_double(s(x)) >= Marked_double(x) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { double(0) >= 0 ; double(s(x)) >= s(s(double(x))) ; double(x) >= +(x,x) ; +(s(x),y) >= s(+(x,y)) ; +(x,0) >= x ; +(x,s(y)) >= s(+(x,y)) ; Marked_+(s(x),y) >= Marked_+(x,y) ; Marked_+(x,s(y)) >= Marked_+(x,y) ; } + Disjunctions:{ { Marked_+(s(x),y) > Marked_+(x,y) ; } { Marked_+(x,s(y)) > Marked_+(x,y) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: double(0) >= 0 constraint: double(s(x)) >= s(s(double(x))) constraint: double(x) >= +(x,x) constraint: +(s(x),y) >= s(+(x,y)) constraint: +(x,0) >= x constraint: +(x,s(y)) >= s(+(x,y)) constraint: Marked_+(s(x),y) >= Marked_+(x,y) constraint: Marked_+(x,s(y)) >= Marked_+(x,y) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] double(0) -> 0 [2] double(s(x)) -> s(s(double(x))) [3] +(x,0) -> x [4] +(x,s(y)) -> s(+(x,y)) [5] +(s(x),y) -> s(+(x,y)) [6] double(x) -> +(x,x) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ Marked_double ] (X0) = 3*X0 + 0; [ s ] (X0) = 1 + 1*X0 + 0; [ double ] (X0) = 2*X0 + 0; [ + ] (X0,X1) = 1*X0 + 1*X1 + 0; ]} { DP termination of: , CRITERION: ORD [ Solution found: polynomial interpretation = [ 0 ] () = 0; [ s ] (X0) = 1 + 1*X0 + 0; [ double ] (X0) = 2*X0 + 0; [ Marked_+ ] (X0,X1) = 3*X0 + 3*X1 + 0; [ + ] (X0,X1) = 1*X0 + 1*X1 + 0; ]} ]} ]} Cime worked for 0.041324 seconds (real time) Cime Exit Status: 0